Finite Group Databasebeta

← #44398902

Subgroups — #44398902

Order 29056.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic454C211yesmaximal, characteristic
2#28409383C211yesmaximal, characteristic, complemented
3#28409328C211yesmaximal, characteristic, complemented
4#28409322C211yesmaximal, characteristic
5#28408779C211yesmaximal, characteristic, complemented
6#28408764C211yesmaximal, characteristic, complemented
7D4⋊C8×C227C211yesmaximal, characteristic
8C22×Dic454—21no—
9#20300288C2211yescharacteristic
10#20300288C2211yescharacteristic
11#20300287—21no—
12#20300267—21no—
13#20300265—22no—
14C4×Dic454C2211yescharacteristic
15D4×Dic227—21no—
16#20300222—21no—
17#20300219—21no—
18C4⋊(C227⋊C8)C2211yescharacteristic
19#20300213—21no—
20#20300213—22no—
21#20300209—21no—
22C4×D4×C227C2211yescharacteristic
23C4⋊C8×C227C2211yescharacteristic
24C4×C8×C227C2211yescharacteristic
25C2×Dic454—22no—
26C2×Dic454—21no—
27C2×Dic454—21no—
28C2×Dic454—42no—
29C2×Dic454—42no—
30C2×Dic454D411yescharacteristic
31C22×Dic227—22no—
32C2×C227⋊C8—21no—
33C4⋊Dic227—21no—
34C4⋊Dic227—21no—
35C4⋊Dic227—21no—
36C4⋊Dic227D412yes—
37C4⋊Dic227D411yescharacteristic
38Dic227⋊C4—22no—
39Dic227⋊C4—21no—
40C22⋊Dic227—22no—
41C4×Dic227—21no—
42C2×D4×C227D411yescharacteristic
43C22×C4×C227—21no—
44C2×C8×C227—21no—
45C2×C8×C227—21no—
46C4⋊C4×C227D411yescharacteristic
47C22⋊C4×C227—21no—
48C42×C227C2311yescharacteristic
49Dic454—21no—
50Dic454—44no—
51Dic454—41no—
52Dic454—41no—
53Dic454—42no—
54Dic454SD1612yes—
55C2×Dic227—21no—
56C2×Dic227—21no—
57C2×Dic227—22no—
58C2×Dic227—44no—
59C2×Dic227—41no—
60C227⋊C8—41no—
61C23×C227—21no—
62D4×C227—21no—
63D4×C227Q1612yes—
64C2×C4×C227—21no—
65C2×C4×C227—41no—
66C2×C4×C227—41no—
67C2×C4×C227C2×D411yescharacteristic
68C2×C4×C227C2×D411yescharacteristic
69C2×C4×C227C2×D411yescharacteristic
70C8×C227—41no—
71C8×C227—41no—
72C22×C227—22no—
73C22×C227—41no—
74C22×C227—41no—
75C22×C227#12011yescharacteristic
76C4×C227—21no—
77C4×C227—41no—
78C4×C227C2×SD1611yescharacteristic
79C4×C227C2×Q1611yescharacteristic
80C4×C227AGL(1,ℤ/8)11yescharacteristic
81C4×C227#13711yescharacteristic
82Dic227—22no—
83Dic227—42no—
84Dic227—41no—
85Dic227—81no—
86C2×C227—42no—
87C2×C227#45011yescharacteristic
88C2×C227#45111yescharacteristic
89C2×C227#45411yescharacteristic
90C227#163711yescharacteristic, complemented, Sylow
91#1637—2271nomaximal, Sylow
92D4×Q8—2271no—
93#487—2271no—
94#477—2271no—
95#476—2271no—
96#332—2271no—
97Q8⋊C8—2271no—
98D4⋊C8D22711yescharacteristic
99C22×Q8—4541no—
100C4⋊Q8—4541no—
101C4⋊Q8—2271no—
102C4⋊Q8—2271no—
103C22⋊Q8—4542no—
104C22⋊Q8—4541no—
105C4×Q8—2271no—
106C4×D4—4541no—
107C4×D4C2×D22711yescharacteristic
108#107—4541no—
109#106—4541no—
110C4⋊C8—2271no—
111C4⋊C8C2×D22711yescharacteristic
112#103—4541no—
113#103—4542no—
114#102—4541no—
115C4×C8C2×D22711yescharacteristic
116C2×Q8—9082no—
117C2×Q8—9082no—
118C2×Q8—4542no—
119C2×Q8—4541no—
120C2×Q8—4541no—
121C2×Q8—2271no—
122C2×D4D90811yescharacteristic
123C22×C4—21no—
124C22×C4—4542no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—4541no—
128C4⋊C4—4542no—
129C4⋊C4—4541no—
130C4⋊C4—4541no—
131C4⋊C4—4541no—
132C4⋊C4—4541no—
133C4⋊C4—2272no—
134C4⋊C4—2271no—
135C4⋊C4D90811yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—4542no—
138C42—4541no—
139C42C22×D22711yescharacteristic
140C23—21no—
141Q8—9082no—
142Q8—9084no—
143Q8—9081no—
144Q8—9081no—
145Q8—4541no—
146Q8—2272no—
147D4—21no—
148D4Dic90812yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—9081no—
153C2×C4—9084no—
154C2×C4—4541no—
155C2×C4—4542no—
156C2×C4—4541no—
157C2×C4D4×D22711yescharacteristic
158C2×C4D4×D22711yescharacteristic
159C2×C4C2×D90811yescharacteristic
160C8—41no—
161C8—41no—
162C8—9081no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2030025811yescharacteristic
167C4—21no—
168C4—41no—
169C4—18161no—
170C4—9082no—
171C4—9081no—
172C4—4542no—
173C4SD16×D22711yescharacteristic
174C4C2×Dic90811yescharacteristic
175C4#2030031211yescharacteristic
176C4#2030032111yescharacteristic
177C2—42no—
178C2#2840918411yescharacteristic
179C2#2840919011yescharacteristic
180C2#2840920611yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC42×C227C23
FrattiniC42C22×D227
FittingD4⋊C8×C227C2
socleC22×C227#120
prime radicalC2×D4×C227D4
hypercenterD4⋊C8D227
hypocenterC227#1637
LCSG ▷ C42×C227 ▷ C22×C227 ▷ C227
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #28409383C2semidirect
3. #28409328C2semidirect
5. #28408779C2semidirect
6. #28408764C2semidirect
90. C227#1637semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D4×Dic4542
#284093832
#284093282
#284093222
#284087792
#284087642
D4⋊C8×C2272
#1637227